Is it possible to paste in edit mode?
You can invoke copy and paste using the Spacebar menu (it shows CtrlV as shortcut for paste, but as you said that doesn't work). Simply press Space and search for copy and paste and use the appropriate entries from the list.


  As pointed out by GiantCowFilms, the copy / paste functions work at object level. So even if you use them in edit mode, the whole object gets duplicated and not your selection!


Because you can use ShiftD to duplicate, there seems to be no need for copy and paste.